Greek Geometry from Thales to EuclidHodges, Figgis, & Company, 1889 - 237 Seiten |
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Seite 33
... μὲν ἄλλο ἀεὶ γίγνεσθαι τὸ εἶδος ὁτὲ δὲ ἕν . Phys . , III . , iv . , p . 203 , 12 . Compare ἀλλ ̓ ἔστι τινὰ αὐξανόμενα ἃ οὐκ ἀλλοιοῦται , οἷον τὸ τετράγωνον γνώμονος περιτεθέντος ηὔξηται μέν , ἀλλοιότερον δὲ οὐδὲν γεγένηται . Cat ...
... μὲν ἄλλο ἀεὶ γίγνεσθαι τὸ εἶδος ὁτὲ δὲ ἕν . Phys . , III . , iv . , p . 203 , 12 . Compare ἀλλ ̓ ἔστι τινὰ αὐξανόμενα ἃ οὐκ ἀλλοιοῦται , οἷον τὸ τετράγωνον γνώμονος περιτεθέντος ηὔξηται μέν , ἀλλοιότερον δὲ οὐδὲν γεγένηται . Cat ...
Seite 61
... μὲν τῶν Πυθαγορείων , διὰ δὲ τὸ ἐξενεγκεῖν , καὶ γράψασθαι πρῶτος σφαῖραν , τὴν ἐκ τῶν δώδεκα ἑξαγώνων [ πενταγώνων ] , ἀπόλοιτο κατὰ θάλατταν , ὡς ἀσεβήσας , δόξαν δὲ λάβοι , ὡς εἶναι δὲ πάντα ἐκείνου τοῦ ἀνδρός · προσαγορεύουσι γὰρ ...
... μὲν τῶν Πυθαγορείων , διὰ δὲ τὸ ἐξενεγκεῖν , καὶ γράψασθαι πρῶτος σφαῖραν , τὴν ἐκ τῶν δώδεκα ἑξαγώνων [ πενταγώνων ] , ἀπόλοιτο κατὰ θάλατταν , ὡς ἀσεβήσας , δόξαν δὲ λάβοι , ὡς εἶναι δὲ πάντα ἐκείνου τοῦ ἀνδρός · προσαγορεύουσι γὰρ ...
Seite 79
... μὲν ἐν τῷ δεσμωτηρίῳ τὸν τοῦ κύκλου τετραγωνισμὸν ypape . Plut . , de Exil . , c . XVII . , vol . III . , p . 734 , ed . Didot . 63 De Arch . , VII . , Praef . 64 Cicero , de finibus bonorum et malorum , I. , c . vi .; Diog . Laert ...
... μὲν ἐν τῷ δεσμωτηρίῳ τὸν τοῦ κύκλου τετραγωνισμὸν ypape . Plut . , de Exil . , c . XVII . , vol . III . , p . 734 , ed . Didot . 63 De Arch . , VII . , Praef . 64 Cicero , de finibus bonorum et malorum , I. , c . vi .; Diog . Laert ...
Seite 86
... μὲν τοῦ κύβου φησὶ γεγονέναι τὴν γῆν , ἐκ δὲ τῆς πυραμίδος τὸ πῦρ , ἐκ δὲ τοῦ ὀκταέδρου τὸν ἀέρα , ἐκ δὲ τοῦ εἰκοσαέδρου τὸ ὕδωρ , ἐκ δὲ τοῦ δωδεκαέδρου τὴν τοῦ παντὸς σφαῖραν . Mλάtwv dè kal èv Toúтois πvbayopícet . Plut . , Plac ...
... μὲν τοῦ κύβου φησὶ γεγονέναι τὴν γῆν , ἐκ δὲ τῆς πυραμίδος τὸ πῦρ , ἐκ δὲ τοῦ ὀκταέδρου τὸν ἀέρα , ἐκ δὲ τοῦ εἰκοσαέδρου τὸ ὕδωρ , ἐκ δὲ τοῦ δωδεκαέδρου τὴν τοῦ παντὸς σφαῖραν . Mλάtwv dè kal èv Toúтois πvbayopícet . Plut . , Plac ...
Seite 113
... the introduction of the phrase ' parallelogram of 33 ἐχέτω δὴ θέσιν κατὰ τὸν τόπον τῆς συμπτώσεως τῶν γραμμῶν τὸ μὲν κινού- μενον ἡμικύκλιον ὡς τὴν τοῦ ΔΚΑ . , & c . I * the cylinder ' ] , yet the whole passage Archytas . 113.
... the introduction of the phrase ' parallelogram of 33 ἐχέτω δὴ θέσιν κατὰ τὸν τόπον τῆς συμπτώσεως τῶν γραμμῶν τὸ μὲν κινού- μενον ἡμικύκλιον ὡς τὴν τοῦ ΔΚΑ . , & c . I * the cylinder ' ] , yet the whole passage Archytas . 113.
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Häufige Begriffe und Wortgruppen
ancient Apollonius Archim Archimedes Archytas Aristaeus Aristotle arithmetic Athens attributed Book Bretsch Bretschneider Cantor circle Cobet cone conic sections construction cube curve Cyzicus Delian Democritus diameter Diog Diogenes Laertius discovery doctrine of proportion dodecahedron Dublin Egyptians Elements equal Eratosthenes Euclid Eudemus Eudoxus Eukl Eutocius extreme and mean figure Friedlein further Geom Gesch given line gnomon Greek Hankel Heiberg Hippias of Elis Hippocrates of Chios History of Geometry Hultsch Iamblichus Ibid incommensurable inscribed Laert lune Math mathematics mean proportionals mean ratio Menaechmus method Montucla Pappus parabola passage Paul Tannery pentagon perpendicular philosophy plane Plato Plutarch probably problem Proclus proof pupil Pyth Pytha Pythagoras Pythagoreans quadrant quadratrix quadrature rectangle referred regular solids right angles right-angled triangles says segments semicircle sides Simplicius solution solved square Tannery Thales Theaetetus theorem tion δὲ καὶ μὲν περὶ τὰ τὴν τῆς τὸ τὸν τοῦ τῶν
Beliebte Passagen
Seite 10 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Seite 145 - ... proclaim it as an authoritative dogma, silencing or disparaging all objectors — that Grecian speculation aspires. To unmask not only positive falsehood, but even affirmation without evidence, exaggerated confidence in what was only doubtful, and show of knowledge without the reality — to look at a problem on all sides, and set forth all the difficulties attending its solution — to take account of deductions from the affirmative evidence, even in the case of conclusions accepted as true...
Seite 219 - The Elements of Geometrie of the most auncient Philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, Citizen of London. Whereunto are annexed certaine Scholies, Annotations, and Inuentions, of the best Mathematiciens, both of time past, and in this our age.
Seite 40 - To divide a given straight line into two parts so that the rectangle contained by the whole and one part shall be equal to the square on the other part...
Seite 76 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Seite 135 - ... the gnomon NOL is equal to C; therefore also AX is equal to C. Wherefore to the straight line AB there is applied the parallelogram AX equal to the given rectilineal figure C, exceeding by the parallelogram PO, which is similar to D, because PO is similar to EL.
Seite 126 - State, they would some day emerge into light. Yes, he said, there is a remarkable charm in them. But I do not clearly understand the change in the order. First you began with a geometry of plane surfaces ? Yes, I said.
Seite 125 - ... solids in revolution, instead of taking solids in themselves; whereas after the second dimension the third, which is concerned with cubes and dimensions of depth, ought to have followed.